Enter the width and height of a rectangle and get its area, perimeter, diagonal length, and the angle the diagonal makes with the base — useful for construction, screens and displays, framing, flooring, and geometry homework.
How it works
The tool applies four standard formulas to the width (w) and height (h) you enter:
- Area = w × h
- Perimeter = 2 × (w + h)
- Diagonal = √(w² + h²) — the Pythagorean theorem, because the diagonal is the hypotenuse of the right triangle formed by the width and height
- Diagonal angle = arctan(h ÷ w), converted to degrees — the angle the diagonal makes with the base
It is unit-agnostic: use any unit consistently and the lengths come out in that unit, the area in square units, and the angle in degrees.
Worked examples
For a rectangle 4 by 3 (a classic Pythagorean triple):
- Area = 4 × 3 = 12
- Perimeter = 2 × (4 + 3) = 14
- Diagonal = √(16 + 9) = √25 = 5
- Diagonal angle = arctan(3 ÷ 4) ≈ 36.87°
For a 16 by 9 rectangle (widescreen display proportions, in any unit):
- Area = 144
- Perimeter = 50
- Diagonal ≈ 18.36
- Diagonal angle ≈ 29.36°
For a 10 by 10 square:
- Area = 100
- Perimeter = 40
- Diagonal = √200 ≈ 14.14 (exactly 10√2)
- Diagonal angle = 45° (always 45° for a square)
| Width | Height | Area | Perimeter | Diagonal | Angle |
|---|---|---|---|---|---|
| 3 | 4 | 12 | 14 | 5 | 53.13° |
| 16 | 9 | 144 | 50 | ~18.36 | 29.36° |
| 10 | 10 | 100 | 40 | ~14.14 | 45° |
| 1920 | 1080 | 2,073,600 | 6,000 | ~2,203 | 29.36° |
Practical applications
Screen size: A “55-inch TV” means the diagonal is 55 inches. If you know the aspect ratio is 16:9, you can work backwards: set width to 16 and height to 9, note the diagonal as ~18.36 units, then scale. The real screen is 55 ÷ 18.36 × 16 ≈ 47.9 inches wide and 27 inches tall.
Flooring and tiling: Multiply area (in square feet or metres) by your material’s coverage rate to get how much flooring to buy. Add 10% waste for cut pieces around edges.
Checking a corner is square: A rectangle is square when the diagonal equals √(w² + h²). If you measure both diagonals of a frame and they are equal, the corners are at 90°. If they differ, one corner is out of square and needs adjustment.
Framing artwork or windows: Perimeter tells you how much material (moulding, gasket, weatherstrip) you need to go around the outside. Diagonal tells you the longest piece you need to cut or carry through a door.
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